Thermal conductance as a probe of the non-local order parameter for a topological superconductor with gauge fluctuations

We investigate the effect of quantum phase slips on a helical quantum wire coupled to a superconductor by proximity. The effective low-energy description of the wire is that of a Majorana chain minimally coupled to a dynamical $\mathbb{Z}_2$ gauge field. Hence the wire emulates a matter-coupled gauge theory, with fermion parity playing the role of the gauged global symmetry. Quantum phase slips lift the ground state degeneracy associated with unpaired Majorana edge modes at the ends of the chain, a change that can be understood as a transition between the confined and the Higgs-mechanism regimes of the gauge theory. We identify the quantization of thermal conductance at the transition as a robust experimental feature separating the two regimes. We explain this result by establishing a relation between thermal conductance and the Fredenhagen-Marcu string order-parameter for confinement in gauge theories. Our work indicates that thermal transport could serve as a measure of non-local order parameters for emergent or simulated topological quantum order.Comment: 5 pages, 2 figures; v2: different introduction, added references, updated figure 2; published version to appear in PR

Nonzero temperature effects on antibunched photons emitted by a quantum point contact out of equilibrium

Electrical current fluctuations in a single-channel quantum point contact can produce photons (at frequency omega close to the applied voltage V x e/hbar) which inherit the sub-Poissonian statistics of the electrons. We extend the existing zero-temperature theory of the photostatistics to nonzero temperature T. The Fano factor F (the ratio of the variance and the average photocount) is 1 for T>T_c (bunched photons). The crossover temperature T_c ~ Deltaomega x hbar/k_B is set by the band width Deltaomega of the detector, even if hbar x Deltaomega << eV. This implies that narrow-band detection of photon antibunching is hindered by thermal fluctuations even in the low-temperature regime where thermal electron noise is negligible relative to shot noise.Comment: 4 pages, 2 pages appendix, 3 figure

Flat-lens focusing of electrons on the surface of a topological insulator

We propose the implementation of an electronic Veselago lens on the conducting surface of a three-dimensional topological insulator (such as Bi2Te3). The negative refraction needed for such a flat lens results from the sign change of the curvature of the Fermi surface, changing from a circular to a snowflake-like shape across a sufficiently large electrostatic potential step. No interband transition (as in graphene) is needed. For this reason, and because the topological insulator provides protection against backscattering, the potential step is able to focus a broad range of incident angles. We calculate the quantum interference pattern produced by a point source, generalizing the analogous optical calculation to include the effect of a noncircular Fermi surface (having a nonzero conic constant).Comment: 6 pages, 6 figure

Where the rocks are in the pond : using critical race theory to gain access to more equitable educational opportunities for African Americans

“Where the rocks are in the pond” is a metaphor for the concept of empowerment so that those who have traditionally been marginalized and isolated, typically people of color and the poor, can learn the normative strategies that the dominant culture accesses to success. Developmentally, members of marginalized populations are harmed by the lack of access to quality resources for social, economic, political and educational growth. I have chosen autoethnography as the vehicle to carry critical events that illuminate the deleterious effects of racialization in U. S. society. The study used critical race theory as the theoretical lens to analyze several narratives of a Black, female educator. These stories and counter-stories intend to increase awareness and understanding in how educational institutions at every level, knowingly or not, participate in the perpetuation of racist policies and practices. The goal of this research is to contribute strategies and techniques to a body of knowledge that speaks little about Black educators navigating the waters in predominately white school settings

Coulomb-assisted braiding of Majorana fermions in a Josephson junction array

We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even-odd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging energies, with exponential sensitivity. By switching the interaction on and off in neighboring segments of a Josephson junction array, the non-Abelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes. This is a solution to the problem how to operate on topological qubits when gate voltages are screened by the superconductor

Coherent pumping of a Mott insulator: Fermi golden rule versus Rabi oscillations

Cold atoms provide a unique arena to study many-body systems far from equilibrium. Furthermore, novel phases in cold atom systems are conveniently investigated by dynamical probes pushing the system out of equilibrium. Here, we discuss the pumping of doubly-occupied sites in a fermionic Mott insulator by a periodic modulation of the hopping amplitude. We show that deep in the insulating phase the many-body system can be mapped onto an effective two-level system which performs coherent Rabi oscillations due to the driving. Coupling the two-level system to the remaining degrees of freedom renders the Rabi oscillations damped. We compare this scheme to an alternative description where the particles are incoherently pumped into a broad continuum.Comment: 4 pages, 3 figure

Anyonic interferometry without anyons: How a flux qubit can read out a topological qubit

Proposals to measure non-Abelian anyons in a superconductor by quantum interference of vortices suffer from the predominantly classical dynamics of the normal core of an Abrikosov vortex. We show how to avoid this obstruction using coreless Josephson vortices, for which the quantum dynamics has been demonstrated experimentally. The interferometer is a flux qubit in a Josephson junction circuit, which can nondestructively read out a topological qubit stored in a pair of anyons --- even though the Josephson vortices themselves are not anyons. The flux qubit does not couple to intra-vortex excitations, thereby removing the dominant restriction on the operating temperature of anyonic interferometry in superconductors.Comment: 7 pages, 3 figures; Added an Appendix on parity-protected single-qubit rotations; problem with Figure 3 correcte

Scattering formula for the topological quantum number of a disordered multi-mode wire

The topological quantum number Q of a superconducting or chiral insulating wire counts the number of stable bound states at the end points. We determine Q from the matrix r of reflection amplitudes from one of the ends, generalizing the known result in the absence of time-reversal and chiral symmetry to all five topologically nontrivial symmetry classes. The formula takes the form of the determinant, Pfaffian, or matrix signature of r, depending on whether r is a real matrix, a real antisymmetric matrix, or a Hermitian matrix. We apply this formula to calculate the topological quantum number of N coupled dimerized polymer chains, including the effects of disorder in the hopping constants. The scattering theory relates a topological phase transition to a conductance peak, of quantized height and with a universal (symmetry class independent) line shape. Two peaks which merge are annihilated in the superconducting symmetry classes, while they reinforce each other in the chiral symmetry classes.Comment: 8 pages, 3 figures, this is the final, published versio

Quantized conductance at the Majorana phase transition in a disordered superconducting wire

Superconducting wires without time-reversal and spin-rotation symmetries can be driven into a topological phase that supports Majorana bound states. Direct detection of these zero-energy states is complicated by the proliferation of low-lying excitations in a disordered multi-mode wire. We show that the phase transition itself is signaled by a quantized thermal conductance and electrical shot noise power, irrespective of the degree of disorder. In a ring geometry, the phase transition is signaled by a period doubling of the magnetoconductance oscillations. These signatures directly follow from the identification of the sign of the determinant of the reflection matrix as a topological quantum number.Comment: 7 pages, 4 figures; v3: added appendix with numerics for long-range disorde

Influence of a random telegraph process on the transport through a point contact

We describe the transport properties of a point contact under the influence of a classical two-level fluctuator. We employ a transfer matrix formalism allowing us to calculate arbitrary correlation functions of the stochastic process by mapping them on matrix products. The result is used to obtain the generating function of the full counting statistics of a classical point contact subject to a classical fluctuator, including extensions to a pair of two-level fluctuators as well as to a quantum point contact. We show that the noise in the quantum point contact is a sum of the (quantum) partitioning noise and the (classical) noise due to the two-level fluctuator. As a side result, we obtain the full counting statistics of a quantum point contact with time-dependent transmission probabilitie